Two firms decide to form a cartel and collude in a way that maximizes industry profits. Each firm has zero production costs and each firm is given a positive output quota by the cartel. Which of the following statement(s) are NOT true.

Question

(a) Each firm would want to produce more than its quota if it knew that the other would continue to produce at its quota.
(b) The price elasticity of demand will be -1 at the output level chosen.
(c) Output will be lower than if the firms behaved as Cournot firms.
(d) Output will be lower than if the firms behaved as competitors.

I pick (a) and (b) because (a) the problem is a shared monopoly meaning that the duopolists know that they earn more when they form a cartel, and (b) states that the firms will produce in the inelastic portion which is not true since they will have negative marginal revenues and total revenues.

Answer 1

The two firms agree to act as a monopolist. Sinc MC is zero for both firms, they will produce where MC=MR=0 (where MR is the combined MR for both firms). And when MR=0, the elasticity of demand is -1. So b is true.

Now at this optimal production point, each firm producing its quota, if a firm decides to produce one more unit the combined MR would become negative. However the overall decline in MR is shared by both firms, while the increase revenue from the one extra unit goes entirely to the cheating firm; profits of the cheating firm go up. So, a is true.

If the firms suddenly switch to a Cournot model, this is the same as scenario a) -- each firm will treat the other's firm's output as fixed. Each firm will want to increase production. So c) is false.

cournot firms are competitors, and since I contend c) is false, d) must also be false.